Method and System for Network Migration Scheduling

ABSTRACT

A method of transforming an ordered list of nodes of a network into one of a plurality of elite ordered lists, the ordered list corresponding to a deloading sequence, the deloading sequence including a temporary capacity requirement, each of the elite ordered lists corresponding to an elite deloading sequence including an elite temporary capacity requirement by generating at least one intermediate ordered list corresponding to an intermediate deloading sequence including an intermediate temporary capacity requirement, selecting one of the intermediate ordered list and the ordered list based on a comparison of the intermediate temporary capacity requirement and the temporary capacity requirement and replacing one of the elite ordered lists with the one of the intermediate ordered list and the ordered list if a value corresponding to one of the intermediate temporary capacity requirement and the temporary capacity requirement is less than a lowest value of the elite temporary capacity requirements.

BACKGROUND

Replacement of outdated communications networks with modern networksimproves the functionality of communications. Such replacement may bedone by substituting one node at a time in a predetermined order. Whennodes are replaced, temporary communications links must be establishedso that nodes that have been upgraded to new technology may communicatewith nodes that have not yet been upgraded and vice versa. By minimizingthe requirements for temporary communications links, the cost of theupgrading process may be optimized.

SUMMARY OF THE INVENTION

A method of transforming an ordered list of nodes of a network into oneof a plurality of elite ordered lists, the ordered list corresponding toa deloading sequence of the nodes from the network, the deloadingsequence including a temporary capacity requirement, each of the eliteordered lists corresponding to an elite deloading sequence including anelite temporary capacity requirement by benerating at least oneintermediate ordered list corresponding to an intermediate deloadingsequence including an intermediate temporary capacity requirement,selecting one of the intermediate ordered list and the ordered listbased on a comparison of the intermediate temporary capacity requirementand the temporary capacity requirement and replacing one of the eliteordered lists with the one of the intermediate ordered list and theordered list if a value corresponding to one of the intermediatetemporary capacity requirement and the temporary capacity requirement isless than a lowest value of the elite temporary capacity requirements.

A system to transform an ordered list of nodes of a network into one ofa plurality of elite ordered lists, the ordered list corresponding to adeloading sequence of the nodes from the network, the deloading sequenceincluding a temporary capacity requirement, each of the elite orderedlists corresponding to an elite deloading sequence including an elitetemporary capacity requirement. The system having a memory storing theordered list of nodes and the elite ordered lists and a processorgenerating at least one intermediate ordered list corresponding to anintermediate deloading sequence including an intermediate temporarycapacity requirement, selecting one of the intermediate ordered list andthe ordered list based on a comparison of the intermediate temporarycapacity requirement and the temporary capacity requirement, andreplacing one of the elite ordered lists with the one of theintermediate ordered list and the ordered list if a value correspondingto one of the intermediate temporary capacity requirement and thetemporary capacity requirement is less than a lowest value of the elitetemporary capacity requirements.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A and 1B show exemplary network diagrams according to the presentinvention.

FIG. 2 shows an exemplary method according to the present invention.

DETAILED DESCRIPTION

The exemplary embodiments of the present invention may be furtherunderstood with reference to the following description and the appendeddrawings, wherein like elements are referred to with the same referencenumerals. The exemplary embodiments of the present invention describesystems and methods for diagnosing problems with network hardware.

The exemplary embodiments of the present invention present methods andsystems for optimizing the process of migrating a data network fromoutdated technology to newer technology. A network may comprise a numberof nodes and arcs connecting the nodes to one another. For example, in aswitch-based network, a node may be a switch and an arc may be a trunkconnecting two switches; in an IP network, a node may be a router and anarc may be an IP path connecting two routers. During the process ofupgrading an outdated network to a new network (e.g., upgrading aswitch-based network to an IP-based network), nodes may be deloaded oneat a time. Deloading is the process of turning off a node in the oldnetwork (e.g., a switch of a switch-based network) and moving all of thetraffic that originates or terminates in that node to a specified nodein the new network (e.g., a router of an IP-based network).

During the migration process, both the old network and the new networkmay be functioning simultaneously. In this situation, there may be sometraffic within the old network, some traffic within the new network, andsome traffic between the two networks. To accommodate the trafficbetween the two networks, capacity must temporarily be made available inthe arcs linking the two networks. The amount of capacity that must bemade available may depend on the sequence in which the switches aredeloaded. The exemplary embodiments of the present invention provide fordetermining a deloading sequence that may minimize this amount ofcapacity. Minimization is desirable in order to reduce the amount oftemporary capacity that must be built, and thus reduce the cost of themigration process.

The exemplary embodiments of the present invention utilize a greedyrandomized adaptive search procedure (“GRASP”) with path-relinking. Theinputs to this procedure may include the set of all nodes in thenetwork, the set of all arcs between nodes in the network, and thecapacity of each arc. The output may be a sequence specifying the orderin which the nodes may optimally be deloaded.

FIG. 1A illustrates an exemplary set of networks according to thepresent invention. A first network 100 may be outdated, while a secondnetwork 150 may be replacing the first network 100. The first network100 may include nodes 110, 112, 114 and 116; as discussed above, thenodes of the first network 100 may be switches. The first network 100may also include arcs 120, 122, 124, 126 and 128 connecting the nodes toone another. As discussed above, for a network 100 in which the nodesare switches, the arcs may be trunks connecting pairs of switches. Thesecond network 150 may include nodes 160, 162, 164 and 166, each ofwhich may correspond to, and be replacing, one of the nodes 110, 112,114 and 116 of the first network 100. As discussed above, the nodes ofthe second network 150 may be routers. The second network 150 may alsoinclude arcs 170, 172, 174, 176 and 178 connecting the nodes to oneanother; as discussed above, arcs of the second network may be IP pathsconnecting two routers. As is the case for the nodes, each of the arcsof the second network 150 may be replacing a corresponding one of thearcs of the first network 100. However, it is noted that a one-to-onecorrespondence between the nodes and arcs of the first network 100 andthe second network 150 is not a requirement of the present invention.

For both of the networks 100 and 150, each of the nodes may be thesource and the destination of a quantity of network traffic. Becauserouting of traffic is predetermined, the capacity of each arc is known.Traffic that originates and terminates within the same network is routedwithin that network. However, during the process of migration, temporarylinks must be established in order to route traffic from one network tothe other. For example, FIG. 1B illustrates the networks of FIG. 1Aafter node 110 of network 100 has been deloaded. Because node 160 ofnetwork 150 may correspond to node 110 of network 100, traffic thatoriginated from or was sent to node 110 may originate from or be sent tonode 160. In order to accomplish this, temporary arcs 192, 194 and 196may need to be established to transmit traffic from, respectively, nodes112, 114 and 116 of network 110 to and from node 160 of network 150.

As those of skill in the art will understand, the amount of traffic thatthe temporary arcs 192, 194 and 196 must be able to handle may besubstantially equivalent to that handled by the arcs 122, 124 and 126 ofthe network 100. Further, those of skill in the art will understand thatbecause each of the arcs may have a predetermined capacity that variesfrom that of the remaining arcs, the amount of temporary capacityrequired when node 110 is deloaded may be different from the amount thatwould be required if another of the nodes of network 100 had beendeloaded. Additionally, as migration continues, the amount of temporarycapacity required, both in total and at any given time, may depend onthe sequence in which the nodes are deloaded. Thus, because buildingtemporary capacity adds to the cost of the migration process, it isdesirable to minimize the amount of required temporary capacity.

The factors to be considered in developing and executing a method orsystem for minimizing the temporary capacity requirements, thus, mayinclude the set of nodes in the two networks, the set of arcs betweenthe nodes, and the capacities of each of the arcs. This may bemathematically modeled as a linear arrangement problem of a graph (V, E,w) wherein V is the set of n vertices (i.e. nodes), E is the set ofedges (i.e. arcs), and w is the vector of edge weights (i.e. arccapacities). A linear arrangement of this graph is a one-to-one functionn: V→{1,2, . . . , n}. For all values of i from 1 to n, the function cutK_(i) between nodes p⁻¹(i) and p⁻¹(i+1) may be defined as the sum of thecapacities of all arcs with one endpoint in p⁻¹(j) and the other inp⁻¹(k) for all values of j=i and k>i. The value K_(max) of the largestcut may be defined as K_(max)=max {K₁, K₂, . . . , K_(n−1)}, whereK_(i)=Σ_({u,ν}εE:π(u)≦i≦90 (ν))w_(uν). The value K_(sum), which is thesum of the cuts, may be defined as

${K_{sum} = {\sum\limits_{i = 1}^{n - 1}\; K_{i}}},$

where K_(i)=Σ_((u,ν)εE)|π(u)−π(ν)·w_(uν)|. The exemplary embodiments ofthe present invention present methods for minimizing both K_(sum) andK_(max).

The exemplary embodiments of the present invention use a GRASP, which isa metaheuristic for finding approximate solutions to combinatorialoptimization problems of the form min{ƒ(x)|x ε X}, where f is theobjective function and X is a discrete set of feasible solutions (i.e.,in this case, a discrete set of possible orders for a finite number ofnodes).

FIG. 2 illustrates an exemplary method 200 according to the presentinvention. In step 210, a data set is received as input. As discussedabove, a data set may include a set of nodes V, a set of arcs E, and aset of arc capacities w. The exemplary method may typically be executedas a computer program; thus, step 210 may be accomplished by, forexample, manual data entry by a user, loading a database into theprogram, etc. The receipt of data in step 210 may also include input bya user of one or more parameters relating to the execution of the method200. The parameters received may include a total number of iterations toperform and an intermediate number of iterations to perform.

In step 220, the nodes are ordered using a greedy randomized algorithm.In this type of algorithm, each of the nodes (e.g., for the network 100,nodes 110, 112, 114 and 116) is evaluated to determine the increase inthe required temporary network capacity that would result from that nodebeing the next added to the ordering. In a non-random greedy algorithm,the single node resulting in the smallest increase in capacity would beautomatically selected. However, using a greedy randomized algorithm, acandidate list is selected from among the nodes being considered (e.g.,the five nodes resulting in the smallest increase, the best 25% of thenodes for causing the smallest increase, etc.), and the node to be addedto the ordering is randomly selected from the candidate list.

The greedy randomized algorithm then continues iterating, with eachiteration operating substantially as described above. At each iteration,the nodes that have not yet been added to the ordering are evaluated todetermine the increase in capacity that would result from theirselection as the next to be added, and a selection is made based on theabove-described greedy randomized process. The result of step 220 is acomplete ordering of the nodes in the network.

Considering the greedy randomized algorithm in more depth, the heuristicbegins by considering an initial sequence of k−1 vertices and adding thek-th vertex to a position where the increase in the objective functionis minimized. The k-th vertex may be selected from any position in thearrangement. The set of k−1 vertices currently in the solution may berepresented as {v₁, . . . , v_(k−1)}, and the current cut values may berepresented as K=K₁, . . . , K_(k−2)}. For a vertex x inserted at thenext position i, the new set of cut values K′={K₁′, . . . , K_(k−1)′}may be calculated as:

$K_{j}^{\prime} = \left\{ \begin{matrix}{K_{j} + {\sum\limits_{a = 1}^{j}\; w_{{xv}_{a}}}} & {{j = 1},\ldots \mspace{11mu},{i - 1}} \\{K_{j - 1} + {\sum\limits_{a = j}^{k - 1}\; w_{{xv}_{a}}}} & {{j = i},\ldots \mspace{11mu},{k - 1}}\end{matrix} \right.$

While such an expression may appear to require O(k²) operations tocompute all k−1 cuts for one given position i, this may be O(k)operations by computing the cuts in the correct order and by storing thevalue of the corresponding cumulative sums

$S_{-} = {{\sum\limits_{a = 1}^{j}\; {w_{{xv}_{a}}\mspace{14mu} {and}\mspace{14mu} S_{+}}} = {\sum\limits_{a = j}^{k - 1}\; {w_{{xv}_{a}}.}}}$

For example, to update the cuts positioned before i, i.e., j=1, . . . ,i−1, it may be convenient to begin by computing K₁ (i.e. j=1), becauseit suffices to add S_=w_(xν) ₁ to the current cut value. To update K₂,the cumulative sum is updated as S_←S_+w_(xν) ₂ and added to the currentcut value. Thus, by starting from j=1, the current cumulative sum may beupdated in O(1) operations, and therefore, each cut value may also berecomputed in O(1) operations. Similarly, for the cuts positioned afteri (i.e., j=i, . . . , k−1), the same time savings may be achieved bybeginning with the last cut K_(k−1) and decreasing j until the i-th cutis reached.

In step 230, a local search is performed on the ordering that isgenerated in step 220. In the local search, each potential pair of nodeswithin the ordering is considered in turn. For each pair of nodes, it isdetermined whether swapping the positions of the two nodes within theordering would improve (i.e., reduce) the total required temporarynetwork capacity. If so, the two nodes are swapped. Once there are nopairs of nodes whose swap reduces the total required capacity, theoutput of step 230 is an ordering of nodes that may be the same as thatoutput by step 220 or may vary either slightly or significantly.

The construction procedure may output an ordering p(1), p(2), . . . ,p(n), n−1 cut values K₁, K₂, . . . , K_(n−1), and for each ν ε V,forward-weighted degrees ƒ(ν)=Σ_(u|π(u)>π(ν))w_(νu) andbackward-weighted degrees b(ν)=Σ_(u|π(u)>π(ν))w_(uν). Local searchexamines all possible vertex swaps in the ordering to find animprovement of the objective function. In other words, it determines howthe swap affects the cut values, and if it improves the objectivefunction, then the swap is made.

If the two nodes swapped as described above are designated as x and y,where x=π⁻¹(i), y=π⁻¹(j), i<j, and f(x),b(x) (with respect to f(y),b(y))are the forward and backward weighted degrees of x (with respect to y)before the swap. Only the cuts K_(i), . . . , K_(j−1) will be affectedby the swap. The nodes between x and y may be designated e_(i+1), . . ., e_(j). The variation of the cut value ΔK(i+a) (a=0, . . . , j−i−1) maybe expressed as:

${\Delta \; {K\left( {i + a} \right)}} = {{b(x)} - {f(x)} + {f(y)} - {b(y)} + {2w_{xy}} + {2{\sum\limits_{k = {i + 1}}^{i + a}\; w_{{xe}_{k}}}} + {2{\sum\limits_{k = {i + a + 1}}^{j - 1}\; w_{{ye}_{k}}}}}$

Using the above expression, the execution time required to recompute thecut values for the above swap may be estimated in terms of the distancebetween x and y in the permutation array. Defining k=j−i+1, the timerequired to compute each new cut value may be O(k), while the timerequired to determine whether the swap improves the solution value maybe O(k²). The execution time may be further improved by calculatingΔK(i+a+1) as a function of ΔK(i+a). This function may be expressed as:ΔK(i+a+1)=ΔK(i+a)+2w_(xe) _(i+a+1) −2w_(yε) _(i+a+1) . Thus, ΔK(i) maybe computed in O(k) operations, and each of the remaining cuts may becomputed in O(1) operations, resulting in all new cut values beingcomputed in O(k) operations. Once the swap has been performed, theweighted forward and backward degrees f(k) and b(k) must be recomputedfor values of k such that i=k=j.

In step 240, the method determines whether the elite set is fullypopulated. An elite set is a group of orderings that consists of thebest orderings that have yet been determined by the algorithm. The sizeof the elite set may be set in advance (e.g., as a parameter specifiedby a user in step 210 of the exemplary method), and may be, for example,10 orderings or 20 orderings. The elite set is initially empty. If theelite set is not yet fully populated, the method proceeds to step 250.If the elite set is fully populated, the method proceeds to step 260.

In step 250, the solution generated by the local search in step 230 isadded to the elite set if it qualifies for inclusion. To qualify forinclusion in the elite set, a solution must be a good one (e.g., it mustresult in a small amount of required extra capacity), and it must bedifferent from other solutions already existing within the elite set.Assuming both of these criteria are satisfied, the solution is added tothe elite set and the method proceeds to step 270.

In step 260, path relinking is performed between the ordering obtainedin step 230 and one of the orderings currently contained in the an eliteset. The solution from the elite set to be used in this step is selectedbased on a weighted randomized selection. Each solution within the eliteset is assigned a weight based on how much it differs from the orderingobtained in step 230. One solution is then selected, with solutions thatdiffer more from the input ordering more likely to be selected.

Path relinking is a process wherein a pair of orderings of nodes arecompared to one another. A set of changes required to be made to a firstof the two orderings in order to transform it into the second of the twoorderings is considered; the output of the path relinking process is theintermediate ordering along the path that provides the minimum value ofthe objective function.

For example, consider two orderings of the nodes of the network 100, afirst ordering {110, 114, 116, 112} and a second ordering {114, 112,110, 116}. One of the orderings was output by step 230, while the otherwas selected from the elite set; the worse of the two orderings isselected as the starting point, while the better of the two is selectedas a guiding solution. Each step in the path between the first orderingand the second ordering will put one of the nodes in the proper placefor the second ordering. For example, one path between the aboveorderings might be:

$\begin{matrix}\left\{ {110,} \right. & {114,} & {116,} & \left. 112 \right\} \\\left\{ {114,} \right. & {110,} & {116,} & \left. 112 \right\} \\\left\{ {114,} \right. & {112,} & {116,} & \left. 110 \right\} \\\left\{ {114,} \right. & {112,} & {110,} & \left. 116 \right\}\end{matrix}$

The objective function is considered for the two intermediate orderings,and if one of the intermediate orderings is better than the firstordering, which was the output of step 220, then it replaces the firstordering. If the intermediate orderings are not better than the firstordering, then the first ordering is the output of the path relinkingprocess.

Those of skill in the art will understand that there are multiplepossible paths between two orderings of a sufficiently large group ofnodes. Referring to the example above, the first step in path relinkingcould be to put any of the nodes 110, 112, 114 or 116 in its properplace in the target order. Each of the four possible first steps mayresult in its own attendant increase or decrease in the objectivefunction. In one exemplary implementation, which is similar to thegreedy ordering process described above, the potential step with thebest possible result (i.e., the greatest decrease or the smallestincrease in the objective function) may be made. In another exemplaryimplementation, which is similar to the greedy randomized processdescribed above, a candidate list may be formed consisting of a numberof the best possible steps, and a move may then be randomly selectedfrom that group.

The above description refers to a “forward” path relinking process; inother words, one wherein the worse of the two solutions being consideredis used as a starting point and the better of the two is used as aguiding solution. Other exemplary implementations may use “backward”path relinking, wherein the better of the two solutions is used as astarting point and the worse is used as a guiding solution. Otherexemplary implementations may truncate the path relinking process inorder to save computation time; truncation may occur, for example,halfway through the process, after a fixed number of steps, once atarget result has been achieved, etc. In still other exemplaryimplementations, “mixed” path relinking may be used. In mixed pathrelinking, forward and backward steps may alternate one step at a time.Finally, in still other implementations, mixed path relinking may betruncated as described above.

Once path relinking is complete, the solution obtained is tested forinclusion into the elite set. The solution is promoted into the eliteset if it meets one of two criteria. First, the solution becomes a partof the elite set if it is better than the best existing solution in theelite set. Second, the solution becomes a part of the elite set if it isbetter than the worst existing solution in the elite set, and issufficiently different from all existing solutions in the elite set. Ineither case, if the solution is added to the elite set, the worstexisting solution is removed from the elite set in order to maintain afixed size. After this decision, the method proceeds to step 270.

In step 270, the method determines whether enough iterations have passedin order to perform intermediate path relinking within the elite set(i.e., the intermediate number of iterations to perform as selected instep 210). If enough iterations have not yet taken place, the methodreturns to step 220. If enough iterations have taken place, the methodcontinues to step 280.

In step 280, path relinking is performed among solutions within theelite set; this process may be referred to as “elite setintensification” or “evolutionary path relinking.” This may be performedamong all pairs of solutions within the elite set, or among a subset ofall possible pairs of solutions. In one embodiment, the best twosolutions within the elite set are selected, and are then path relinkedwith one another as well as with each of the remaining solutions withinthe elite set. Each new solution obtained by such path relinking istested for inclusion into a new, “second generation” elite set, and isincluded in the new elite set if it meets the criteria for inclusioninto an elite set as described above.

As should be apparent, the number of possible solutions thus consideredmay be twice the number of solutions in the “first generation” elite set(for embodiments where the best two solutions in the first generationelite set are compared to the remaining solutions), may be the square ofthe number of solutions in the first generation of the elite set (forembodiments where each solution in the first generation of the elite setis compared to every other solution), or may be some other function ofthe number of solutions in the first generation elite set (for otherembodiments). However, in order to keep processing times reasonable, itis desirable for the number of solutions in the second generation eliteset to be the same as the number in the first generation elite set.Thus, once the target number of solutions have been added to the secondgeneration elite set, newly considered solutions are evaluated in thesame way as described above in step 260.

Once all desired pairs have been considered and the second generationelite set is fully populated, it is compared to the first generationelite set. If the best solution in the second generation elite set is animprovement over the best solution in the first generation elite set(i.e., if it results in less required added capacity), the process isrepeated as above. Path relinking is performed among pairs of solutionsin the second generation elite set to form a third generation elite set,followed by later generations if necessary. However, if there is noimprovement from the previous generation to the next generation (e.g.,from the second generation to the third generation), the new generation(e.g., the third generation) is used as the elite set and step 280concludes.

In step 290, it is determined whether enough iterations have passed forthe method to terminate. In one implementation of the present invention,this number of iterations may be preselected, such as by user inputduring step 210. In another implementation, iterations may continueuntil a certain target has been reached. If not enough iterations havepassed, the method returns to step 220 to perform more GRASP iterationsand generate new solutions. If enough iterations have passed, the methodterminates; the output is the best solution contained in the elite set.The output may then be returned to a user (e.g., by display on a monitoror other display device, by printing, etc.).

The exemplary embodiments of the present invention may enable adetermination to be made of an optimal ordering for the deloading ofnodes during network migration. The optimal ordering may then be used tominimize the required temporary network capacity that must beconstructed, thus reducing the cost of the migration process. Totalcapacity reduction achieved may be on the order of a 30% improvementover a baseline solution.

The present invention has been described with reference to the abovespecific exemplary embodiments. However, those of ordinary skill in theart will recognize that the same principles may be applied to otherembodiments of the present invention, and that the exemplary embodimentsshould therefore be read in an illustrative, rather than limiting,sense.

1. A method of transforming an ordered list of nodes of a network intoone of a plurality of elite ordered lists, the ordered listcorresponding to a deloading sequence of the nodes from the network, thedeloading sequence including a temporary capacity requirement, each ofthe elite ordered lists corresponding to an elite deloading sequenceincluding an elite temporary capacity requirement, comprising:generating at least one intermediate ordered list corresponding to anintermediate deloading sequence including an intermediate temporarycapacity requirement; selecting one of the intermediate ordered list andthe ordered list based on a comparison of the intermediate temporarycapacity requirement and the temporary capacity requirement; andreplacing one of the elite ordered lists with the one of theintermediate ordered list and the ordered list if a value correspondingto one of the intermediate temporary capacity requirement and thetemporary capacity requirement is less than a lowest value of the elitetemporary capacity requirements.
 2. The method of claim 1, furthercomprising: replacing one of the elite ordered lists with the one of theintermediate ordered list and the ordered list if the valuecorresponding to one of the intermediate temporary capacity requirementand the temporary capacity requirement is less than a greatest value ofthe elite temporary capacity requirements and the one of theintermediate ordered list and the ordered list differs from each of theelite ordered lists by at least a predetermined value.
 3. The method ofclaim 1, wherein the transforming is based on a greedy randomizedprocess.
 4. The method of claim 1, further comprising: transforming afirst one of the elite ordered lists into each of the remaining ones ofthe elite ordered lists, the transforming generating at least oneintermediate elite ordered list for each of the remaining ones of theelite ordered lists, each of intermediate elite ordered listscorresponding to an intermediate elite deloading sequence including anintermediate elite temporary capacity requirement.
 5. The method ofclaim 4, further comprising: comparing the lowest value of the elitetemporary capacity requirements to a lowest value of the intermediateelite temporary capacity requirements; and outputting the intermediateelite ordered list corresponding to the lowest value of the intermediateelite temporary capacity requirements, if the lowest values are equal.6. The method of claim 5, further comprising: repeating the transformingof claim 4 for the intermediate elite ordered lists if the lowest valueof the elite temporary capacity requirements is greater than the lowestvalue of the intermediate elite temporary capacity requirements.
 7. Themethod of claim 6, wherein a number of times the repeating is performedis limited by a predefined threshold.
 8. The method of claim 1, furthercomprising: generating an original ordered list of nodes, the originalordered list corresponding to an original deloading sequence includingan original temporary capacity requirement; modifying the originalordered list to generate a modified ordered list of the nodes, themodified ordered list corresponding to a modified deloading sequenceincluding a modified temporary capacity requirement; and selecting, asthe ordered list, one of the original ordered list and the modifiedordered list based on a comparison of the original temporary capacityrequirement and the modified temporary capacity requirement.
 9. Themethod of claim 8, wherein the selecting is based on the one of theoriginal ordered list and the modified ordered list that corresponds toa lower value of one of the original temporary capacity requirement andthe modified temporary capacity requirement.
 10. The method of claim 8,wherein the generating is based on a greedy randomized search procedure.11. A system to transform an ordered list of nodes of a network into oneof a plurality of elite ordered lists, the ordered list corresponding toa deloading sequence of the nodes from the network, the deloadingsequence including a temporary capacity requirement, each of the eliteordered lists corresponding to an elite deloading sequence including anelite temporary capacity requirement, comprising: a memory storing theordered list of nodes and the elite ordered lists; and a processorgenerating at least one intermediate ordered list corresponding to anintermediate deloading sequence including an intermediate temporarycapacity requirement, selecting one of the intermediate ordered list andthe ordered list based on a comparison of the intermediate temporarycapacity requirement and the temporary capacity requirement, andreplacing one of the elite ordered lists with the one of theintermediate ordered list and the ordered list if a value correspondingto one of the intermediate temporary capacity requirement and thetemporary capacity requirement is less than a lowest value of the elitetemporary capacity requirements.
 12. The system of claim 11, wherein theprocessor replaces one of the elite ordered lists with the one of theintermediate ordered list and the ordered list if the valuecorresponding to one of the intermediate temporary capacity requirementand the temporary capacity requirement is less than a greatest value ofthe elite temporary capacity requirements and the one of theintermediate ordered list and the ordered list differs from each of theelite ordered lists by at least a predetermined value.
 13. The system ofclaim 11, wherein the processor transforms the ordered list based on agreedy randomized process.
 14. The system of claim 11, wherein theprocessor transforms a first one of the elite ordered lists into each ofthe remaining ones of the elite ordered lists, the transforminggenerating at least one intermediate elite ordered list for each of theremaining ones of the elite ordered lists, each of intermediate eliteordered lists corresponding to an intermediate elite deloading sequenceincluding an intermediate elite temporary capacity requirement.
 15. Thesystem of claim 14, wherein the processor compares the lowest value ofthe elite temporary capacity requirements to a lowest value of theintermediate elite temporary capacity requirements and outputs theintermediate elite ordered list corresponding to the lowest value of theintermediate elite temporary capacity requirements, if the lowest valuesare equal.
 16. The system of claim 15, wherein the processor repeats thetransforming of claim 14 for the intermediate elite ordered lists if thelowest value of the elite temporary capacity requirements is greaterthan the lowest value of the intermediate elite temporary capacityrequirements.
 17. The system of claim 11, wherein the processorgenerates an original ordered list of nodes, the original ordered listcorresponding to an original deloading sequence including an originaltemporary capacity requirement, modifies the original ordered list togenerate a modified ordered list of the nodes, the modified ordered listcorresponding to a modified deloading sequence including a modifiedtemporary capacity requirement and selects, as the ordered list, one ofthe original ordered list and the modified ordered list based on acomparison of the original temporary capacity requirement and themodified temporary capacity requirement.
 18. The system of claim 17,wherein the processor selects the ordered list based on the one of theoriginal ordered list and the modified ordered list that corresponds toa lower value of one of the original temporary capacity requirement andthe modified temporary capacity requirement.
 19. The system of claim 17,wherein the processor generates the original ordered list of nodes basedon a greedy randomized search procedure.
 20. A memory storing a set ofinstructions executable by a processor to transform an ordered list ofnodes of a network into one of a plurality of elite ordered lists, theordered list corresponding to a deloading sequence of the nodes from thenetwork, the deloading sequence including a temporary capacityrequirement, each of the elite ordered lists corresponding to an elitedeloading sequence including an elite temporary capacity requirement,the set of instructions being operable to: generate at least oneintermediate ordered list corresponding to an intermediate deloadingsequence including an intermediate temporary capacity requirement;select one of the intermediate ordered list and the ordered list basedon a comparison of the intermediate temporary capacity requirement andthe temporary capacity requirement; and replace one of the elite orderedlists with the one of the intermediate ordered list and the ordered listif a value corresponding to one of the intermediate temporary capacityrequirement and the temporary capacity requirement is less than a lowestvalue of the elite temporary capacity requirements.